Show that the small angular deviation ε of a plumb line from the true vertical (i.e., toward the center of Earth) at a point on Earth's surface at a latitude λ is
ε=g0−Rω2cos2λRω2sinλcosλ
where R is the radius of Earth. What is the value (in seconds of arc) of the maximum deviation? Note that the entire denominator in the answer is actually the effective g, and g0 denotes the pure gravitational component.